$\cot^{-1}\left(- frac{1}{\sqrt{3}} ight) = $

Question

$\cot^{-1}\left(-	frac{1}{\sqrt{3}}ight) = $

Accepted Answer

C. $	frac{2\pi}{3}$

$\cot^{-1}$ has principal range $(0, \pi)$.
At $	heta = 	frac{2\pi}{3}$, $\cot	heta = 	frac{\cos(2\pi/3)}{\sin(2\pi/3)} = 	frac{-1/2}{\sqrt{3}/2} = -	frac{1}{\sqrt{3}}$.
**Option D ($5\pi/6$) yields $\cot = -\sqrt{3}$, not $-1/\sqrt{3}$ — common trap.**

Answer

$	frac{\pi}{3}$

Answer

$-	frac{\pi}{3}$

Answer

$	frac{5\pi}{6}$

$\cot^{-1}\left(-\tfrac{1}{\sqrt{3}}\right) = $

Keep practising Unit 1A3: Function Composition and Inverses